induction effects for heterochromatic brightness matching, heterochromatic flicker photometry, and...

Induction effects for heterochromatic brightnessmatching, heterochromatic flicker photometry,

and minimally distinct border: implications for theneural mechanisms underlying induction

Karen L. Gunther*

Department of Neuroscience, Oberlin College, Oberlin, Ohio 44074

Karen R. Dobkins

Department of Psychology, University of California, San Diego, La Jolla, California 92093

Received December 14, 2004; revised manuscript received April 21, 2005; accepted April 24, 2005

Brightness induction refers to the finding that the apparent brightness of a stimulus changes when sur-rounded by a black versus a white stimulus. In the current study, we investigated the effects of black/whitesurrounding stimuli on settings made between red and green stimuli on three different tasks: heterochromaticbrightness matching (HBM), heterochromatic flicker photometry (HFP), and minimally distinct border (MDB).For HBM, subjects varied the relative luminance between the red and green stimuli so that the brightness ofthe two colors appeared equal. For the two other tasks, matches were made based on minimizing red/greenflicker (HFP) or the saliency of a red/green border (MDB). For all three tasks, the presence of black/white sur-rounding stimuli significantly altered red/green settings, demonstrating the existence of induction effects.These results are discussed in terms of which underlying color pathways (L+M versus L−M) may contributeto induction effects for the different tasks. © 2005 Optical Society of America

OCIS codes: 330.4270, 330.5510.

1. INTRODUCTIONBrightness induction, first described in 1839,1 refers tothe finding that the apparent brightness of an object is in-fluenced by the context in which it is presented. In thesimplest example of brightness induction, a gray disk sur-rounded by a black annulus appears brighter than thesame gray disk surrounded by a white annulus. This re-sult is interpreted as the annulus inducing the brightnessof the central disk. A simple way to quantify the magni-tude of induction is to employ an ‘‘achromatic brightnessmatching’’ (ABM) task, in which subjects are asked to ad-just the luminance of a gray test disk (presented by itself)to match the apparent brightness of a gray disk sur-rounded by a black or white annulus. In various forms ofthis task, subjects have been found to need more lumi-nance in the gray test disk if the comparison disk is sur-rounded by a black annulus than if the comparison disk issurrounded by a white annulus.2–5

In the current study, we investigated induction effectsby employing chromatic (red versus green), rather thangray, test stimuli. Our stimuli consisted of red and greenstimuli presented alone or surrounded by inducing whiteand black stimuli (see Fig. 1). Akin to the ABM task de-scribed above, our subjects conducted a heterochromaticbrightness matching (HBM) task, adjusting the relativeluminance of the red versus green stimuli so that the twocolors appeared equally bright,6 both in the absence andin the presence of surrounding inducing stimuli. Induc-tion is shown if the red/green luminance ratio at

equibrightness is altered by the presence of the inducers.The induction effects obtained on the HBM task werecompared with those obtained on two other tasks: hetero-chromatic flicker photometry (HFP) and minimally dis-tinct border (MDB). In the HFP task, subjects viewed astimulus flickering between red and green (both in the ab-sence and in the presence of surrounding black/whitestimuli) and adjusted the relative luminance of the twocolors until the percept of flicker was least salient.7–9 Inthe MDB task, subjects viewed red and green stimuliplaced in spatial juxtaposition (both in the absence and inthe presence of surrounding black/white stimuli) and ad-justed the relative luminance of the two colors until theborder between them was least salient.10 Note that unlikefor HBM, for HFP and MDB the subject’s task does notinvolve comparing any property of the red versus greenstimulus per se. However, common to all three tasks, theobtained settings provide a measure of equality betweenthe red and the green. To reflect this commonality, we usea single term, equality settings, to describe the settingsmade for all three tasks. What is thought to actually beequated between the red and the green is the amount ofneural response elicited by the two stimuli within the rel-evant color pathway(s) of the visual system.

Three postreceptoral pathways have been described incolor vision. The L+M pathway (referred to as the lumi-nance pathway) signals a weighted sum of long-wavelength-sensitive (L) and medium-wavelength-sensitive (M) cones [with some debate regarding the

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contribution of short-wavelength-sensitive (S) cones11–13].The L−M pathway (referred to as the red/green chro-matic pathway) signals a difference between L and Mcones. The S− �L+M� pathway (referred to as the tritanchromatic pathway) signals a difference between S conesand the sum of L and M cones. The HFP and MDB tasksdescribed above are thought to rely exclusively on signalsin the L+M pathway, and thus HFP and MDB settingsare typically referred to as equiluminance settings. At thepoint of minimal flicker (or minimal border), the two col-

ors employed (for example, red and green) are thought toelicit equal neural responses within the L+M pathway.The equating of neural responses elicited by red andgreen on a task that relies on the L+M pathway (such asHFP or MDB) can be described mathematically as

PLLr + PMMr = PLLg + PMMg, �1�

where Lr and Mr refer to the L- and M-cone responses, re-spectively, elicited by the red stimulus; Lg and Mg refer to

Fig. 1. Stimuli used in these experiments. A. Alternating disk and annulus stimulus used in Experiments 1 and 2. Shown is the in-duction condition in which a red disk surrounded by a white annulus (time t1) was alternated with a green disk surrounded by a blackannulus (time t2; referred to as the green–black condition). The red–black induction condition (not shown) consisted of the disk andannulus in the opposite phase relationship. The noninduction condition (not shown) consisted only of the central disk alternating be-tween red and green. “Red” and “green” and “t1,” “t2,” are shown here to aid the reader and were not present in the actual stimulus. B.Red/green grating with black/white flankers stimulus used in Experiment 3. Shown is the induction condition in which the black stripeswere spatially in phase with the green stripes (referred to as the green–black condition). The red–black induction condition (not shown)consisted of the black stripes spatially in phase with the red stripes. The noninduction condition (not shown) consisted only of the red/green grating. Some conditions used temporally reversing gratings. Some conditions used static stimuli (as shown here). Note that therewere slight differences in the stimulus depending on whether the task was HFP (which used sinusoidal gratings), HBM (which usedsquare wave gratings and a thin black line at the red/green borders), and MDB (which used square wave gratings, shown here). See textfor further details.

K. L. Gunther and K. R. Dobkins Vol. 22, No. 10 /October 2005 /J. Opt. Soc. Am. A 2183

the cone responses elicited by the green stimulus; and PLand PM are weighting factors that refer to the relativeproportion of L and M cones, respectively.14 In contrast toHFP and MDB, HBM is thought to rely on a combinationof signals in all three color pathways, L+M,L−M, andS− �L+M�. Together, these pathways are thought to con-stitute the brightness mechanism, and, accordingly, HBMsettings are typically referred to as equibrightness set-tings. In the case of HBM, two colors will be perceived asequally bright when some combination of the responseswithin the three color pathways elicited by the two colorsis equated.

Under conditions of induction, i.e., when the red andgreen stimuli are surrounded by white and black stimuli,respectively (or vice versa), the neural responses to redand green (and the equating thereof) are expected to bemodulated. Note that we assume that this modulation oc-curs within the color pathway(s) that underlies the taskitself. Staying with the example from Eq. (1), in which thetask is one that relies on the L+M pathway, this modula-tion can be described mathematically as

�PLLr + PMMr�*X = �PLLg + PMMg�*Y, �2�

where X and Y are proportional to the summed L- plusM-cone excitation produced by the white and the blackannulus, respectively. Consider the case where red is sur-rounded by white and green by black. Conceptually, thewhite surround stimulus should inhibit (i.e., decrease) theneural response to the red test stimulus compared withthe case where the red stimulus is presented alone. Toimplement this in Eq. (2), the X on the left side of theequation would take a value less than 1.0. Conversely, theblack surround stimulus might facilitate (i.e., increase)the neural response to the green test stimulus comparedwith the case where the green stimulus is presentedalone. To implement this in Eq. (2), the Y on the right sideof the equation would take a value greater than 1.0. [Notethat the modulatory surround effects in Eq. (2) maploosely onto center/surround receptive field organizationknown to exist for ganglion cells in the retina and cells ofthe LGN. Although the size of receptive fields in theretina and the LGN are clearly smaller than the stimuliused in our experiment, it is reasonable to assume thatsome cells with receptive fields falling at the borders ofthe center and surround are affected in this manner andcould contribute to the induction phenomenon.] Thus, apair of red and green stimuli that produce equallyweighted sums of L- and M-cone activity in the absence ofblack/white inducing stimuli [Eq. (1)] cannot produceequally weighted sums in the presence of the inducingstimuli [Eq. (2)]. In the presence of inducing stimuli(white surrounding red, black surrounding green), to cre-ate an equal response to red and green, Lr and Mr wouldneed to be increased (which the subject achieves by in-creasing the luminance of the red stimulus), or Lg and Mgwould need to be decreased (which the subject achieves bydecreasing the luminance of the green stimulus), or both.The difference in the red/green luminance ratio in thepresence versus the absence of the inducing stimuli istermed the induction effect.

We set out to investigate the contribution of the differ-ent color pathways to induction. To simplify our study, we

restricted our investigation to the L+M and L−M path-ways (by using stimuli that do not modulate the S cones).In Experiment 1, we measured induction effects on theHFP task. Although HFP is thought to rely only on theL+M pathway, this is likely to be restricted to high tem-poral frequencies; at low temporal frequencies, both L+M and L−M are likely to contribute9,15 (see below andSection 4). For this reason, we employed a range of tem-poral frequencies (4–28 Hz), including those high enoughto eliminate contribution from the L−M pathway (i.e.,greater than 10–15 Hz). The results of this experiment re-vealed significant induction effects on red/green equalitysettings, indicating that induction effects can occur ex-plicitly within the L+M pathway. In Experiments 2 and3, we compared the magnitude of induction effects pro-duced across the three different tasks (HFP, HBM, andMDB) as a means to investigate the relative degree of in-duction occurring within the L+M versus L−M path-ways. For these experiments, we used lower temporal fre-quencies (0–4 Hz) because it is very difficult to conductHBM and MDB above �4 Hz. Here we found comparablemagnitudes of induction effects for the HFP and HBMtasks but significantly smaller induction effects for theMDB task. This result can be explained by proposing thatat low temporal frequencies, induction effects on HFP andHBM equality settings invoke both the L+M and L−Mpathways (whose signals add together), while inductioneffects on MDB settings rely only on signals within theL+M pathway. This hypothesis is further supported bythe results from correlational analyses performed in Ex-periment 3, which showed that the magnitude of induc-tion effects for HFP and HBM correlated positively witheach other but not with the magnitude of induction effectsfor MDB.

2. METHODSThese experiments measured red/green settings for threedifferent tasks: HFP, HBM, and MDB. Although HFP andMDB settings are typically called “equiluminant” andHBM settings are typically called “equibright” (see Sec-tion 1), in the current study we refer to the settings ob-tained from all three tasks as “equality settings” to stayagnostic regarding the mechanisms (i.e., luminance ver-sus brightness) contributing to these settings. Also notethat our use of the term equality settings is meant to re-flect the fact that the red/green setting for a given task ispresumably that which produces an equal neural re-sponse to the red and green stimulus within the colorpathways that are involved in that task (see Section 1).Data were obtained in three separate experiments. Ex-periment 1 addressed whether red/green equality settingsobtained using HFP are susceptible to the induction ef-fects of a black/white surround and whether these induc-tion effects vary across temporal frequencies. The stimu-lus consisted of a disk alternating between red and green,surrounded by an annulus alternating between black andwhite (in phase with the red/green alternation). Experi-ment 2, which used the same stimuli as in Experiment 1,addressed whether the magnitude of induction effects onequality settings obtained using HFP differ from those ob-tained using HBM. In Experiment 3, we compared the


magnitude of induction effects on equality settings for allthree tasks (HFP, HBM, and MDB). Here we used red/green gratings (rather than disk stimuli) because theMDB task requires the presence of a red/green border.

A. SubjectsA total of 29 subjects participated as either volunteers orpaid research subjects in the three separate experiments.All had normal or corrected-to-normal vision and normalred/green color vision as assessed by the Ishihara Testsfor Colour Deficiency. Both Experiments 1 and 2 includedfive subjects (Experiment 1 age range, 19 to 34 years;mean, 23.8±6.0 years. Experiment 2 age range, 17 to 34years; mean, 23.8±6.3 years). Twenty-two subjects par-ticipated in Experiment 3 (age range, 21 to 40 years;mean, 27.9±4.6 years). Note that the reason for the largenumber of subjects in Experiment 3 was to allow us toconduct correlation analyses on the data. First authorKLG participated in all three experiments, and researchassistant BDA participated in Experiments 1 and 2. Withthe exception of these two subjects, all other subjects werenaïve to the purpose of the study.

B. ApparatusFor all experiments, visual stimuli were generated inMatlab (The MathWorks, Inc.), interfaced with stimulussoftware (version 6.111) from Cambridge Research Sys-tems (CRS). In Experiments 1 and 2 these were presentedon a ViewSonic P95f monitor (19-in. display, 1024�768 pixels, 100 Hz refresh) driven by a CRS VSG 2/4video board. The 15-bit video board allowed for 32,768discrete luminance levels. In Experiment 3, visual stimuliwere presented on an NEC MultiSync FE750� monitor(17-in. display, 1024�768 pixels, 100 Hz refresh) drivenby a CRS VSG 2/3 video board. This 12-bit video boardallowed for 4096 discrete luminance levels. For all experi-ments, the maximum output for the monitor wascalibrated to equal-energy white (CIE chromaticity coor-dinates � 0.333, 0.333), and the voltage/luminance rela-tionship was linearized independently for each of thethree guns in the display, using a Gamma Correction Sys-tem and an OptiCAL 256M (CRS).

C. StimuliIn Experiment 1, we obtained HFP equality settings.Stimuli (see Fig. 1A) consisted of a disk (3.5° diameter)that counterphase-reversed (temporal sinusoidal) be-tween red [CIE coordinates � 0.354, 0.325; MacLeod–Boynton (M–B) coordinates: M/L=0.320,S=0.016] andgreen (CIE coordinates � 0.311, 0.345; M–B: M/L=0.350; S=0.016), through equal-energy white (CIE coor-dinates =0.333, 0.333; M–B coordinates: M/L=0.335,S=0.016) at a mean luminance of 28 cd/m2. This alterna-tion modulated the L cones and M cones by 2.28% and4.15%, respectively, resulting in a rms cone contrast of3.35%. Note that the red/green colors were chosen to se-lectively modulate the L and M cones, while keeping theS-cone excitation constant. The purpose of silencingS-cone modulation was to eliminate the contribution ofthe S− �L+M� (tritan) color pathway, allowing us to selec-tively study the contribution of the L+M (luminance) and

L−M (red/green) color pathways. The background was ofthe same mean chromaticity and luminance as the red/green disk.

The disk was presented in three different configura-tions. In the first, the noninduction condition, it was pre-sented by itself. In the two other conditions, the inductionconditions, the disk was surrounded by an annulus (6° di-ameter) that counterphase-reversed (temporal sinu-soidal), in phase with the red/green disk reversal, be-tween black �0 cd/m2� and white �56 cd/m2�. The meanluminance �28 cd/m2� and chromaticity (equal-energywhite) of the annulus matched that of the alternating red/green disk and of the background. The Michelson contrast��Lumwhite−Lumblack� / �Lumwhite+Lumblack�� produced byalternating the annulus was 100%, which translates intoa cone contrast in L and M cones of 100%. In one induc-tion condition, the black phase of the annulus was tempo-rally in phase with the green phase of the disk [which werefer to as the green–black condition; see Fig. 1A]. In theother induction condition, the black phase of the annuluswas temporally in phase with the red phase of the disk(which we refer to as the red–black condition). The disk/annulus stimulus was presented at seven different tem-poral frequencies: 4, 8, 12, 16, 20, 24, and 28 Hz. Notethat because the vertical refresh of our monitor was 100Hz, the temporal sinusoids for the higher temporal fre-quencies in this experiment were necessarily sparselysampled, and therefore the temporal modulation in thesecases would have been closer to a square wave than to asine wave. This should have the effect of producing highertemporal frequency harmonics in the stimulus (althoughthese harmonics will be of lower amplitude). In addition,in the case where the temporal frequency both was highand did not divide evenly into 100 Hz (e.g., 28 Hz), thesampling would have been somewhat irregular. We be-lieve that these temporal sampling artifacts (sparse or ir-regular sampling) had negligible effects on the resultsfrom Experiment 1 since we observed systematic effects ofincreasing temporal frequency on the magnitude (and di-rection) of induction (see Section 3). Although we do notfeel that these temporal sampling artifacts affected thedata in Experiment 1, we did see substantial individualdifferences across subjects in the magnitude of inductioneffects at temporal frequencies higher than 4 Hz. For thisreason, in Experiment 2, we tested subjects only at andbelow 4 Hz.

In Experiment 2, we obtained both HFP and HBMequality settings using disk/annulus stimuli with thesame spatial configurations as those employed in Experi-ment 1 (see Fig. 1A). In this experiment, HFP settingswere obtained at 4 Hz, and HBM settings were obtainedat 4 Hz and 0.5 Hz. Our reason for using a 0.5 Hz condi-tion for HBM was to try to match as nearly as possible the0 Hz temporal frequency used in previous HBM studies,i.e., where settings are made using two simultaneouslypresented static fields (e.g., one red, one green). The useof temporally alternating stimuli in the current HBMtask was required in order to use the same stimulus con-figuration as was used for HFP, where a single diskstimulus was presented and red/green comparisons weremade over time.


In Experiment 3, we obtained HFP, HBM, and MDBequality settings using vertically oriented �0.5 c/deg�gratings (see Fig. 1B) that were either counterphase-reversed (temporal sinusoid) or static. In the noninduc-tion condition, the stimulus consisted of red/green grat-ings presented in a rectangular (5° horizontal by 1.5°vertical) aperture, which was similar in area �7.5 deg2� tothe red/green disk employed in Experiments 1 and 2�9.6 deg2�. The gratings were presented with the zerocrossing positioned in the center of the stimulus to ensureequal number of red and green stripes in the stimulus. Inthe two induction conditions, black/white gratings (size:5° horizontal � 1.5° vertical) appeared juxtaposed aboveand below, and were spatially in phase with, the red/green grating. In the green–black induction condition, theblack phase of the flanking luminance grating wasaligned with the green phase of the red/green grating (seeFig. 1B), analogous to the green–black disk/annulus ar-rangement of Experiments 1 and 2. In the red–black in-duction condition, the black phase was aligned with thered phase of the red/green grating. As with the diskstimulus in Experiments 1 and 2, the red/green gratingsin Experiment 3 were modulated through equal-energywhite (CIE coordinates � 0.333, 0.333; M–B coordinates:M/L=0.335,S=0.016), at a mean luminance of 28 cd/m2,and produced 3.35% rms cone modulation in L and Mcones, while the S-cone excitation was kept constant. Likethe black/white annulus in Experiments 1 and 2, theflanking black/white gratings in Experiment 3 weremodulated 100% and were the same mean luminance andchromaticity as the red/green gratings.

In Experiment 3, we obtained settings for HFP (at 4Hz), HBM (at 4 and 0 Hz), and MDB (at 4 and 0 Hz). Notethat unlike in Experiment 2, 0 Hz, rather than 0.5 Hz,was employed for the HBM task in Experiment 3, as theuse of red/green gratings allowed the red-versus-greenbrightness comparison to be made spatially, without theneed for temporal alternation. Also note that the stimuliin Experiment 3 varied slightly with task, as follows. Inthe HFP task, the gratings were spatially sinusoidal,whereas in the HBM and MDB tasks, the gratings werespatially square wave. Square waves were needed in theMDB to provide a border for subjects to minimize. Squarewaves are also commonly used for the HBM task. Whilesubjects were performing the HBM task, we added asingle-pixel-width vertical black line separating eachphase of the grating to prevent subjects from attemptingto minimize the border.10

D. ParadigmFor all experiments, subjects were tested in a dark room,viewed the video display binocularly from a chin rest situ-ated 57 cm away, and were instructed to maintain fixationon a central black dot. For all tasks (HFP, HBM, andMDB) subjects adjusted the red/green luminance contrastto meet a specific criterion (defined differently for eachtask; see below). As explained above, for all tasks we referto the red/green setting at this criterion as the equalitypoint. Subjects made these adjustments in either coarsesteps (2.5% Michelson contrast) or fine steps (0.5% Mich-elson contrast), depending on how near they were to theequality point, using specified toggle switches on a re-

sponse box. Note that we are restricted to describing theproperties of our red/green stimuli in terms of luminancecontrast ��Lumred−Lumgreen� / �Lumred+Lumgreen��, sincemonitor calibration is necessarily in units of luminance.This is not to be confused with the concept of luminanceas one of the three color pathways.

In Experiment 1, subjects made HFP equality settings.On each trial, the disk stimulus appeared centered on thefixation dot, and the subject adjusted the luminance con-trast between the red and the green phases until the per-cept of flicker was least salient. HFP settings were ob-tained at seven different temporal frequencies (4–28 Hz).It is perhaps important to point out that HFP settings, al-though thought to be difficult at low temporalfrequencies,16 are nonetheless possible (i.e., flicker canstill be minimized). At times the stimulus looks almostiridescent—simultaneously red and green without flicker-ing between the two, an effect that Boynton and Kaiser17

referred to as a “flickerless exchange” or a “temporal ana-log of the melting borders reported in minimally distinctborder.” Data were obtained for each of three stimulusconfigurations: one noninduction condition (no annulus)and two induction conditions (red–black and green–black). Subjects were tested in blocks of ten trials, with asingle condition presented per block. The order of presen-tation of the 21 blocks of trials (seven temporal frequen-cies � three stimulus configurations) was randomizedacross subjects. The equality point for each subject andeach condition was determined from the mean settingacross ten trials. For each subject, six to eight hours wererequired to complete the entire experiment, with testingdivided into 1.5- to 4-hour blocks.

In Experiment 2, subjects made HFP settings at 4 Hzand HBM settings at 4 Hz and 0.5 Hz. On an HFP trial,settings were made as described for Experiment 1. On anHBM trial, the disk stimulus appeared centered on thefixation dot, and the subject adjusted the luminance con-trast between the red and the green phases until the twocolors were perceived to be equally bright. HFP and HBMsettings were performed for each of the three stimulusconfigurations: one noninduction condition (no annulus)and two induction conditions (red–black and green–black). Subjects were tested in blocks of ten trials, with asingle condition presented per block. For the duration ofeach block, the appropriate task instructions appeared atthe top of the screen (i.e., “minimize flicker” or “matchbrightness”). The order of presentation of the 18 blocks(one HFP frequency � three stimulus configurations+ two HBM frequencies � three stimulus configurations,two ten-trial blocks/condition) was randomized acrosssubjects. Equality points for each subject and each condi-tion were determined from the mean setting across 20 tri-als. For each subject, 6 to 15 h were required to completethe entire experiment, with testing divided into 1.5- to2.5-hour blocks.

In Experiment 3, subjects made HFP settings at 4 Hz,HBM settings at 4 Hz and 0 Hz, and MDB settings at 4Hz and 0 Hz. On an HFP or an HBM trial, settings weremade as described for Experiments 1 and 2. On an MDBtrial, the subject adjusted the luminance contrast be-tween the red and the green phases of the grating untilthe borders between the two were least salient. HFP,


HBM, and MDB settings were performed for each of threestimulus configurations: one noninduction condition (noflanking luminance grating) and two induction conditions(red–black and green–black). Subjects were tested inblocks of 16 trials, with a single condition presented perblock. For the duration of each block, the appropriate taskinstructions appeared at the top of the screen (i.e., “mini-mize flicker,” “match brightness,” or “minimize border”).The order of presentation of the 15 blocks (one HFP fre-quency � three stimulus configurations + two HBM fre-quencies � three stimulus configurations + two MDB fre-quencies � three stimulus configurations) wasrandomized across subjects. Equality points for HFP,HBM, and MDB for each subject and each condition weredetermined from the mean setting across 16 trials. Foreach subject, 3.5 to 9.5 h were required to complete theentire experiment, with testing divided into 1.5- to 2-hblocks.

E. Data AnalysisThere were two main measures in this study. (1) Red/green equality settings (HFP, HBM, and MDB) for the dif-ferent temporal frequencies and induction conditions.These values are expressed in terms of Michelson lumi-nance contrast. (2) Induction effects. For each task/temporal frequency, an induction effect was calculated asthe difference in luminance contrast between a subject’sred/green setting in the induction condition (red–black orgreen–black) and the noninduction condition. In Experi-ment 1, there were substantial individual differences inthe magnitude and direction of the induction effect as afunction of temporal frequency, and thus data were notcombined across subjects. This was not an issue in Ex-periments 2 and 3, so here data were averaged across sub-jects. In addition, because the magnitude of the inductioneffect in Experiments 2 and 3 was found to be statisticallyindistinguishable for the red–black versus green–blackinduction conditions, the absolute values of the magni-tudes of induction were averaged for each subject beforeaveraging across subjects.

3. RESULTSA. Experiment 1: Investigating Induction Effects on HFPSettingsHFP settings for the disk stimulus (Fig. 1A) are plotted asa function of temporal frequency (4–28 Hz) in Fig. 2. Dataare presented separately for the noninduction condition(diamonds) and the two induction conditions: red–black(squares), green–black (circles). Equality settings are pre-sented in terms of luminance contrast between the redand green ��Lumred−Lumgreen� / �Lumred+Lumgreen��, withzero denoting photometric equiluminance �V��, positivevalues denoting red-more-luminous-than-green, andnegative values denoting green-more-luminous-than-red.Note that data are presented separately for the five sub-jects (rather than obtaining a group mean), since the ef-fects of temporal frequency on induction effects werefound to differ across individuals.

In the noninduction condition, equality settings wereessentially constant, and were close to photometric equi-

luminance �V��, across temporal frequencies. This lack ofa temporal frequency effect runs contrary to previousstudies that have shown temporal frequency effects onHFP settings obtained by using gratings.9,15 The discrep-ancy suggests that some interaction of temporal fre-quency and spatial structure (gratings versus disks) couldinfluence HFP settings.

Induction effects can be observed by comparing data inthe noninduction condition with those in the two induc-tion conditions. Here we found that at the lowest tempo-ral frequency tested (4 Hz), all subjects exhibited induc-tion effects in the predicted direction. For example, in thegreen–black induction condition (i.e., when the green andred phases of the disk were in phase with the black andwhite annuli, respectively, circles), luminance contrasts ofthe red/green equality settings were more positive thanthose observed in the noninduction condition (diamonds).These settings indicate that subjects had to increase therelative luminance of the red disk to make a match to thegreen disk. Presumably this occurred, as displayed in Sec-tion 1 in Eq. (2), because the black annulus surroundingthe green disk increases the neural response to the greendisk while the white annulus surrounding the red disk de-creases the neural response to the red disk, and thus toequate the neural response elicited by the red and green,the luminance of the red disk must be increased to com-pensate. Likewise, an induction effect at 4 Hz in the red–black induction condition (squares) is evidenced by thefact that equality settings were less positive in this con-dition compared with those observed in the noninductioncondition (although the effects in the red–black conditiondo not appear as strong as those in the green–black con-dition).

Most interesting in these data is the fact that the effectof the black/white annulus varied systematically withtemporal frequency; results were consistent with an in-duction effect, no effect, or a reversal of the induction ef-fect, depending on temporal frequency. And, the temporalfrequencies at which these different effects occurred var-ied across subjects. A reversal in the induction effect,which occurred at the higher temporal frequencies (spe-cifically for subjects KLG, FA, and TO), is evidenced bythe fact that the luminance contrasts of the equality set-tings in the green–black condition were less positive thanthose observed in the noninduction condition (and viceversa for the red–black condition). At first glance, this re-versal could be interpreted as the black/white annulusproducing assimilation effects (e.g., that a black annulussurrounding a green disk decreases the neural response tothe green disk), which is conceptually the opposite of aninduction effect. We believe, however, that a more likelyreason for this reversal is that it reflects true inductionbut that at (or before) the stage in visual processingwhere induction occurs, there exists a response lag be-tween the processing of the alternating red/green diskstimulus and the alternating black/white annulus. At lowtemporal frequencies (i.e., 4 Hz), this response lag will beinconsequential, producing induction effects in the pre-dicted direction. At some higher temporal frequency, theresponse lag between the processing of the disk and an-nulus will produce a 1/4 cycle phase shift between them,


which will result in no effect of the annulus (since thetime-average luminance of the annulus during the pro-cessing of both the red and green disks will be gray). Atsome even higher temporal frequency, the response lagbetween the processing of the disk and annulus will pro-duce a 1/2 cycle phase shift between them. This will pro-duce a reversal in the psychophysically measured induc-tion effect, which will masquerade as an assimilationeffect. This account can explain the systematic variationin effects of the black/white annulus as temporal fre-quency is increased. Note that in two of three subjectswho showed a reversal effect, as the temporal frequency

was increased even further the reversal effect either wentaway (subject TO), which suggests a 3/4 cycle phase shift,or reversed again to produce results in the predicted di-rection for induction (subject KLG), which suggests a fullcycle phase shift. Even in subjects who did not show aclear reversal effect (subjects AIM and BDA), there was aloss of the induction effect, followed by a re-emergence, astemporal frequency was increased. And, for subject BDA,at even higher temporal frequencies (around 28 Hz), theinduction effect disappeared again, which suggests a oneand one fourth cycle phase shift between the processing ofthe alternating red/green disk and the alternating black/

Fig. 2. (Color online) HFP data from Experiment 1. Plotted for each of the five subjects are HFP equality settings as a function oftemporal frequency, for one noninduction condition (diamonds) and two induction conditions: red–black (squares) and green–black(circles). Equality settings are presented in terms of luminance contrast between the red and the green ��Lumred−Lumgreen� / �Lumred+Lumgreen��, with zero denoting photometric equiluminance �V��, positive values denoting red-more-luminous-than-green and negativevalues denoting green-more-luminous-than-red. Error bars, often smaller than the symbols, represent ±1 SEM (standard error of themean).


white disk.In sum, the results from Experiment 1 demonstrate in-

duction effects of a black/white annulus on HFP equalitysettings. However, the effects of the black/white annulusvaried with temporal frequency and inconsistently fromone subject to another (presumably because the degree ofresponse lag varies across subjects). We return to possibleneural substrates for this result in Section 4. The excep-tion to this were data obtained at 4 Hz, where all subjectsshowed the same pattern of results, i.e., induction effectsin the predicted direction. For this reason, Experiments 2and 3 were conducted at frequencies of 4 Hz or lower.

B. Experiment 2: Comparing the Magnitude of InductionEffects on HFP versus HBM SettingsIn this experiment, we used the same stimuli as in Ex-periment 1 but compared the magnitude of induction ef-fects on HFP versus HBM equality settings. Group meanequality settings (obtained at 4 Hz for both HFP andHBM and at 0.5 Hz for HBM) are plotted in Fig. 3A interms of luminance contrast between the red and green(error bars denote ±1 SEM). Data are presented sepa-

rately for the noninduction condition (diamonds) and thetwo induction conditions that contained the black/whiteannulus: red–black (squares) and green–black (circles).

These data reveal that in the noninduction condition,equality settings (at both temporal frequencies) were sta-tistically indistinguishable �F�2,8�=1.229,p=0.3424�,and all values were close to photometric equiluminance�V��. With regard to induction effects, these data showthat for all three task/temporal frequency conditions(HFP at 4 Hz, HBM at 4 and 0.5 Hz), the effects of theblack/white annulus were in the predicted direction. Thatis, the green–black condition (circles) yielded red/greenequality settings that were more positive than those ob-served for the noninduction condition (diamonds), whilethe red–black condition (squares) yielded settings thatwere less positive. To evaluate more directly the effects ofthe black/white annulus on red/green equality settings,we plot collapsed induction effects in Fig. 3B. The induc-tion effect was calculated as the absolute difference in lu-minance contrast between the red/green setting in the in-duction condition (red–black or green–black) and thenon–induction condition. Because the magnitude of the

Fig. 3. (Color online) HFP and HBM Data from Experiment 2. A. Group mean HFP (at 4 Hz) and HBM equality settings (at 0.5 and 4Hz) are plotted in terms of red/green luminance contrast for one noninduction condition (diamonds) and two induction conditions: red–black (squares) and green–black (circles). B. Group mean induction effects are plotted for the different conditions (see text for details).Error bars represent ±1 SEM.


induction effects were found to be statistically indistin-guishable for the red–black versus green–black inductionconditions (t-test p-values were all �0.12), data for thetwo were averaged for each subject before averagingacross subjects. For all three task/temporal frequencyconditions (HFP at 4 Hz, HBM at 4 and 0.5 Hz), inductioneffects were significant, as evidenced by values signifi-cantly greater than zero (p�0.0027 for all conditions,1-tailed t-test, which passed the Bonferroni corrected � of0.0167, i.e., 0.05/3 conditions). In addition, there was nosignificant difference in the magnitude of induction effectacross the one HFP and two HBM conditions �F�2,8�=0.297,p=0.7508�.

These results from Experiment 2 replicate the resultsfrom Experiment 1, demonstrating induction effects of ablack/white annulus on HFP equality settings. In addi-tion, these results show that the magnitude of inductioneffects are statistically indistinguishable on the HBM ver-sus HFP tasks. We return to possible explanations forthese results in Section 4.

C. Experiment 3: Comparing the Magnitude of InductionEffects on HFP, MDB, and HBM SettingsIn this experiment, we added another measure for equal-ity, MDB. Owing to the nature of the MDB task, weneeded to use stimuli containing red/green borders, andtherefore this experiment employed red/green gratings(see Section 2 and Fig. 1B). Group mean HFP settings (ob-tained at 4 Hz), MDB settings (obtained at 4 and 0 Hz),and HBM settings (obtained at 4 and 0 Hz) are plotted inFig. 4A (error bars denote ±1 SEM). Data are presentedseparately for the noninduction condition (diamonds) andthe two induction conditions: red–black (squares), green–black (circles). In the noninduction condition, a significanteffect of condition was found �F�4,84�=10.745,p=0.0001�. Post-hoc analyses revealed that this was drivenby a difference between HBM settings at 0 Hz and allother settings. With regard to induction effects, the effectsof the black/white annulus were in the predicted direc-tion, i.e., the green–black condition (circles) yielded red/green equality settings that were more positive than

Fig. 4. (Color online) HFP, HBM, and MDB data from Experiment 3. A. Group mean HFP (at 4 Hz), HBM (at 0 and 4 Hz), and MDB (at0 and 4 Hz) equality settings are plotted in terms of red/green luminance contrast for one noninduction condition (diamonds) and twoinduction conditions: red–black (squares) and green–black (circles). B. Group mean induction effects are plotted for the different condi-tions (see text for details). Error bars represent ±1 SEM.


those observed for the noninduction condition (diamonds),while the red-black condition (squares) yielded settingsthat were less positive.

To evaluate more directly the effects of the black/whiteannulus on red/green equality settings, we plot inductioneffects in Fig. 4B. Because induction effects were found tobe statistically indistinguishable for the red–black versusgreen–black induction conditions (t-test p-values were all�0.27), data for the two were averaged for each subjectbefore averaging across subjects. For all five task/temporal frequency conditions (HFP at 4 Hz, HBM at 4and 0 Hz, MDB at 4 and 0 Hz), induction effects were sig-nificant, as evidenced by values significantly greater thanzero (p�0.00002 for all conditions, 1-tailed t-tests, whichpassed the Bonferroni corrected � of 0.01, i.e., 0.05/5 con-ditions). These significant induction effects for HFP andHBM settings replicate those observed in Experiments 1and 2. Interestingly, however, the overall magnitude ofthe induction effects was much smaller in Experiment 3than in Experiments 1 and 2, by a factor of about 3. Thisdifference is likely due to differences in spatial structure(or dominant spatial frequency) between the experiments,since previous studies have shown that spatial param-eters can affect the magnitude of induction.4,18 That is,Experiment 3 used gratings of 0.5 c/deg (i.e., each stripewas 1° in width), while Experiments 1 and 2 used a disk/annulus of 3.5° and 6° diameter, respectively. In addition,in Experiments 1 and 2, the red and green disks werefully surrounded by the annulus (black or white), while inExperiment 3, each red and green stripe of the gratingwas flanked by a black or white stripe only at the top andbottom.

The results from Experiment 3 revealed no significantdifference between the magnitude of induction effects inthe one HFP and two HBM conditions �F�2,42�=3.185,p=0.0515�, a finding that is in line with those from Experi-ment 2. However, the magnitudes of the induction effectsfor the MDB task were significantly smaller than thoseobtained on both the HFP and HBM tasks. This was con-firmed by collapsing induction effects across the one HFPand two HBM conditions and comparing the result withinduction effects collapsed across the two MDB conditions[paired, 1-tailed t�21�=2.20, p=0.00004]. We return topossible explanations for these results in Section 4.

D. Experiment 3: Correlating the Magnitude of InductionEffects on HFP, MDB, and HBM across SubjectsAs a way of addressing whether common or separatemechanisms underlie the induction effects on the differ-ent tasks/temporal frequencies, we performed correlationanalyses on the magnitude of the induction effect ob-tained across our 22 subjects in Experiment 3. The logicbehind these analyses is that tasks/temporal frequenciesfor which induction effects are correlated across subjectsare likely to be mediated by the same underlying mecha-nisms, whereas tasks/temporal frequencies for whichinduction effects are not correlated across subjects arelikely to be mediated by separate underlyingmechanisms.19 The results from these analyses are shownin Fig. 5 in a table format. These analyses reveal twomain findings. First, there were significant positive corre-lations (speckled boxes) between the one HFP condition (4

Hz) and the two HBM conditions (4 Hz and 0 Hz), sug-gesting that the induction effects for these two tasks (andtwo different frequencies for HBM) are subserved by com-mon underlying mechanisms. Second, the magnitudes ofinduction effects for HFP and HBM did not correlate posi-tively with those for MDB (at either 0 or 4 Hz), suggestingthat induction effects for HFP and HBM are subserved byseparate mechanisms than are induction effects for MDB.In fact, MDB induction effects at 0 Hz correlated nega-tively with HBM induction effects at both 0 and 4 Hz(gray boxes). This negative correlation indicates thatthere is an inverse relationship between the extent of in-duction occurring in mechanisms subserving induction onthe HBM versus MDB task and perhaps, by transitivity,also between HFP and MDB. We return to possible expla-nations for this relationship in Section 4.

4. DISCUSSIONSeveral previous studies have demonstrated brightnessinduction; i.e., the apparent brightness of a stimuluschanges when surrounded by black versus white stimuli.In the current study, we replicated this basic finding byemploying HBM, demonstrating significant effects ofblack/white inducing stimuli on the apparent brightnessof red versus green test stimuli. In addition, the currentstudy demonstrated significant induction effects on red/green settings obtained from two other tasks, HFP, andMDB. For these tasks, subjects adjusted the luminancecontrast between the red and green stimuli in order to ei-ther minimize flicker (HFP) or minimize the salience of aborder (MDB). These induction effects observed for HFPand MDB suggest that brightness induction can occureven when subjects are not comparing the apparentbrightness of two colors per se.

For the remainder of this discussion, we address poten-tial mechanisms underlying our results. Specifically, weaddress the relative contributions of two of the three colorpathways in vision: the L+M (luminance) pathway andthe L−M (red/green chromatic) pathway. Note that thecontribution from the third color pathway [S− �L+M�, ortritan] is discussed only briefly in this section, as thestimuli in the current study were designed to isolate thecontribution of the L+M and L−M pathways. We beginby discussing evidence from previous studies suggestingthat HFP and MDB settings rely exclusively on theL+M pathway, while HBM settings rely on both L+Mand L−M pathways. Note that this discussion will be

Fig. 5. Pearson r values for the magnitude of induction effectsacross different tasks/temporal frequencies: HFP 4 Hz, HBM 0Hz, HBM 4 Hz, MDB 0 Hz, and MDB 4 Hz. Significant positiveand negative correlations are depicted by speckled and grayboxes, respectively. Single asterisks denote p�0.05; double aster-isks denote p�0.01.


based on data obtained at the prototypical temporal fre-quency for each task (i.e., HFP at 15 Hz, MDB at 0 Hz,and HBM at 0 Hz). We then discuss results from the cur-rent study, addressing the degree to which the observedinduction effects, some of which were obtained at nontypi-cal temporal frequencies for a given task, rely on the dif-ferent color pathways.

A. Potential for Rod ContributionBefore proceeding with the discussion, we address thepossibility that signals in the rod photoreceptors contrib-uted to our results. The mean luminance employed in thecurrent study �28 cd/m2� may not have been high enoughto saturate the rods completely,20 and thus our red/greenstimuli may have modulated activity in the rods by asmuch as 15% for red/green stimuli at photometric equilu-minance. (This value was obtained by convolving thespectral radiance of the red phase of our stimuli with thescotopic spectral sensitivity. This value was subtractedfrom the value calculated from the green phase of thestimulus, the difference of which was then divided by thesum of the two.) However, at least for red/green settingsobtained in the noninduction conditions of the currentstudy, our results suggest that the rod contribution wasminimal, if not absent, for two reasons. First, if rods con-tributed, red/green settings should have been biasedaway from photometric equiluminance (specifically, to-ward needing more red to match the green). This was notthe case for any Experiment, 1, 2, or 3 (see diamonds inFig. 2–4). Second, if rods contributed to red/green set-tings, their influence should have fallen off substantiallywith increasing temporal frequency, with the result thatred/green settings would vary with temporal frequency.21

Contrary to this prediction, red/green settings obtainedfrom the HFP task in Experiment 1 were clearly constantacross a large range of temporal frequencies (4 to 28 Hz).

Although it is more difficult to determine whether therods were involved in the induction effects of the currentstudy, we would deem it unlikely given their negligible ef-fects on red/green settings in the absence of inducingstimuli. More importantly, we would argue that rod con-tribution (had it existed) does not bear on the issue ofwhich postreceptoral pathways, L+M,L−M, or both, me-diate our results, since neurophysiological studies haveshown that rods provide input to both pathways.22,23

Given the intermingling of rod and cone signals at thepostreceptoral level, it is likely that both rod and cone sig-nals can contribute to induction effects revealed psycho-physically. This possibility is supported by recent findingsthat a surround stimulus that isolates the rods can alterthe apparent brightness of a center stimulus that isolatesthe cones (and vice versa).24

B. Color Pathways Underlying HFP, MDB, and HBMSettings: Evidence from Previous LiteratureIn this subsection, we discuss which color pathways(L+M versus L−M) are thought to underlie red/green set-tings obtained with HFP, MDB, and HBM under the typi-cal testing conditions employed for each task. For allthree, we refer to the red/green settings as ‘‘equality set-tings’’ since the assumption is that a setting reflects an

equal neural response elicited by the red and by the greenphases of the stimulus within the color pathway(s) thatare involved in that task.

There are three main lines of evidence suggesting thatHFP at relatively high temporal frequencies ��15 Hz� re-lies exclusively on signals in the L+M pathway. First, thespectral sensitivity function (also referred to as the lumi-nous efficiency function, or V�) produced by using HFP tomatch monochromatic lights across the visible spectrumto a reference light (often white) is well modeled by aweighted sum of the L- and M-cone spectra.25,26 Second,when HFP is conducted at 15 Hz, the conscious perceptionof “color” is obliterated, i.e., the stimulus appears as grayflicker. Because it is the L−M, and not the L+M, pathwaythat is thought to signal color per se (“red” or “green”),this result suggests that the L−M pathway is not in-volved in HFP settings at 15 Hz. Third, neurophysiologi-cal studies in macaques (whose visual systems are verysimilar to that of humans) have concluded that phasicretinal ganglion cells (which receive L+M input and arethus considered the neural substrate for the L+M colorpathway), and not tonic retinal ganglion cells (which re-ceive L−M input and are thus considered the neural sub-strate for the L−M color pathway), underlie human HFPsettings.16 Analogous to minimizing flicker in HFP, Lee etal.16 measured the luminance of a monochromatic lightnecessary to minimize neural response when this lightwas alternated (at 10 Hz) with a reference light. Takenacross wavelengths, this yields the spectral sensitivitycurve of the neuron. Phasic cells yielded clear minima andyielded spectral sensitivity curves that mirrored those ob-tained psychophysically by using HFP in humans. By con-trast, tonic cells did not yield clear response minima atany relative radiance of the test and reference light. Thustheir responses did not correlate with, and were deemedunlikely to account for, HFP settings revealed psycho-physically.

In addition to the fact that tonic �L−M� cell responsesat 10 Hz do not correlate with HFP settings, there is an-other reason why tonic cell responses are thought un-likely to contribute to HFP settings, at least for HFP con-ducted at relatively high temporal frequencies. It isbelieved that high-temporal-frequency tonic cell signalsare lost downstream because they pass through a strin-gent temporal filter at the cortical level (corner frequency�5 Hz, whereas the signals from phasic cells passthrough a cortical temporal filter with a much higher cor-ner frequency, �20 Hz27,28). Where in visual cortex thisfiltering occurs is not clearly known. One study hasshown that some chromatically opponent �L−M� cells inV1 can still follow high temporal frequencies.29 Thus thefiltering might occur past V1, yet at an early enough stageof processing that does not reach conscious perception.Also note that this temporal filtering of tonic cell signalspresumably explains why the colors of a flickering stimu-lus are not perceivable at high temporal frequencies (seeabove).

Like HFP at 15 Hz, MDB (which is typically performedon static, 0 Hz, stimuli) is thought to rely exclusively onsignals in the L+M pathway. This is because, like HFP,the V� spectral sensitivity curve yielded by MDB at 0 Hzcan be modeled by a weighted sum of the L- and M-cone


spectra. That is, HFP settings at 15 Hz and MDB settingsat 0 Hz yield identical V� spectral sensitivity curves.30

Also, like the neural data described above for HFP set-tings, neurophysiological studies in macaques have dem-onstrated that phasic �L+M� retinal ganglion cells yieldclear response minima to chromatic borders at relative in-tensities that mirror MDB settings obtained psychophysi-cally in humans.31 By contrast, tonic �L−M� retinal gan-glion cells do not yield clear response minima at anyrelative intensity of the colors making up the chromaticborder, and thus their responses are unlikely to contrib-ute to MDB settings. Together, these data suggest thatMDB settings rely on signals in the L+M, and not theL−M, pathway.

In contrast to HFP and MDB, HBM settings (which aretypically performed on static, 0 Hz, stimuli) are thoughtto rely on signals in both the L+M and L−M pathways[as well as the S− �L+M� pathway]. The best known evi-dence for this notion comes from comparing the spectralsensitivity curve obtained from HFP (i.e., the V� curve)with that obtained by using HBM (referred to as thebrightness function). The brightness function, althoughvery similar to V�, is wider and has a characteristic dip atabout 570 nm, known as the Sloan notch. The brightnessfunction can be thought of as the V� function (produced bythe L+M pathway) over which is added the sensitivityfrom the L−M and S− �L+M� pathways. The trough of theSloan notch occurs at a wavelength where L- and M-conesare equally excited, and thus the notch is explained by thefact that the L−M component is zero at this point.32 Thatsignals in the L−M pathway contribute to HBM settingsis also supported by results showing that HBM settingsare influenced by chromatic annuli33,34 and the state ofchromatic adaptation.35 Further, results from severalstudies that have modeled HBM data by computing theweights of the color pathway inputs support contributionfrom all three36–40 (but see Refs. 41–43 for discrepanciesregarding whether all pathways contribute). In sum, theHBM brightness function is thought of as a composite ofactivity in all three color pathways.

C. Which Color Pathways Underlie Induction: L+M,L−M, or Both?Because brightness settings (such as those obtained inHBM) are thought to rely on signals in both the L+M andthe L−M color pathways, it is reasonable to assume thatinduction effects on brightness settings likewise occurwithin both the L+M and the L−M pathways. However,it is also logically possible that brightness induction reliesexclusively on signals within one of these two pathways.To date, two neurophysiological studies have investigatedthe neural substrate for brightness induction, one incats44,45 and one in macaque monkeys.46 Using achro-matic stimuli, these investigators found that the responseof some V1 and LGN neurons to stimuli placed in theirreceptive field is enhanced when flanking stimuli of lowerluminance are placed just outside the receptive field (andvice versa, i.e., that responses are diminished when theflanking stimuli are of higher luminance), in a mannerthat mirrors brightness induction revealed psychophysi-cally. Unfortunately, because the Rossi et al.44,45 studieswere performed in cats, who do not possess a chromati-

cally opponent L−M pathway, these neurophysiologicaldata do not allow us to address whether L+M,L−M, orboth underlie induction effects. The Kinoshita andKomatsu46 study, although utilizing monkeys who do pos-sess the L−M pathway, did not address this issue.

Below, we discuss how the psychophysical data of thecurrent study, which employed tasks thought to rely se-lectively on responses in the L+M pathway or on both theL+M and the L−M pathways, might be used to answerthe question of which color pathways are involved in in-duction effects.

D. Evidence for Induction in the L+M PathwayIn Experiment 1 of the current study, we observed induc-tion effects for HFP settings over a range of temporal fre-quencies (4–28 Hz), which included those typically em-ployed in HFP experiments ��15 Hz�. Because responsesin the L−M pathway should be obliterated (as a result oftemporal filtering in cortex) above at least 15 Hz, our re-sults provide evidence that induction effects can occur ex-clusively within the L+M pathway. In addition, Experi-ment 1 showed that induction effects waned and waxed astemporal frequency was increased. As discussed in Sec-tion 3, we believe that this temporal frequency effect re-flects the existence of a response lag between the process-ing of the alternating red/green disk stimulus and thealternating black/white annulus. It is likely that the re-sponse lag results from the fact that the red/green disk inour study was of much lower contrast (3.35% cone con-trast) than that of the black/white annulus (100% conecontrast), since previous neurophysiological studies haveshown that response latencies in visual areas (such as V1)decrease with increasing stimulus contrast.47,48 This ef-fect of contrast on response latency has also been reportedfor magnocellular cells (which receive input from phasicretinal ganglion cells) in primate LGN.49 This result isparticularly relevant given that magnocellular cells, likephasic retinal ganglion cells (see above), are consideredpart of the neural substrate for the L+M color pathway.That is, the known existence of responses lags in the L+M pathway is consistent with the notion that the effectof temporal frequency on the induction effect is occurringin the L+M pathway.

Like the current study, previous studies have reportedthat the magnitude of brightness induction decreaseswith increasing temporal frequency.45,50–54 However, un-like Experiment 1 of the current study, in which red/greensettings were made using the HFP (minimal flicker) task,these previous studies used achromatic stimuli in bright-ness matching tasks. In addition, these previous studiestested only up to the point at which induction ‘‘disap-pears’’ (4–10 Hz, depending on the study). None of thesestudies went to higher frequencies, where they, too, mighthave revealed the reversal and/or re-emergence of the in-duction effect observed in the current study. Also unlikethe current study, the previous studies did not interpretthe observed effects of temporal frequency on induction interms of response lags between the processing of the in-ducer and the inducee. For example, Rossi and Paradiso52

accounted for decreasing induction effects with increasingtemporal frequency by proposing that induction effectsare based on a filling-in process that takes time. They


suggested that the induction effect of the annulus beginsat the border between the disk and annulus, spreadingover time to affect the entire disk. At higher temporal fre-quencies, they suggested, there is not enough time for thefilling-in process to be completed, and thus the inductioneffect is diminished. This explanation, however, cannotaccount for the results of Experiment 1 of the currentstudy, where induction effects re-emerged as temporal fre-quency was increased further.

E. Evidence for Induction in the L−M PathwayAlthough none of the tasks in the current study were de-signed to isolate the L−M pathway, we might be able toestimate the degree of induction occurring in the L−Mpathway by comparing the magnitude of induction pro-duced in a task that relies only on the L+M pathway withthe magnitude of induction produced in a task that relieson both the L+M and the L−M pathways. Here the as-sumption is that induction effects within the L+M and,the L−M pathways are summed, so that the magnitude ofinduction effect for a task that relies on both pathways ispredicted to be larger than the magnitude of induction ef-fect for a task that relies on just the L+M pathway. Onthe basis of data from previous studies (see Subsection4.B, above), the HFP/MDB and HBM tasks performed inExperiments 2 and 3 of the current study would seem tofulfill these roles. However, the assumption that HFP re-lies exclusively on the L+M pathway may require thatthe HFP stimulus alternate at a high enough temporalfrequency to obliterate responses generated in the L−Mpathway (by temporal filtering at the cortical level; seeabove). At lower temporal frequencies, such as those em-ployed in Experiments 2 and 3 (i.e., 4 Hz), L−M signalscould contribute to HFP settings. Despite the lack of neu-rophysioloigcal data bearing on this question (i.e., neuralcorrelates for HFP settings have been investigated usingonly relatively high, 10 Hz, stimuli; see above), resultsfrom several previous psychophysical studies (includingfrom our own laboratory) do seem to suggest that HFPsettings at 4 Hz rely on responses in both the L+M andthe L−M pathways.9,15,35 Presumably, these psychophysi-cal HFP settings are based on minimizing the differencebetween the combined responses within the two pathwaysto the red versus the green phase of the stimulus. On thebasis of these previous studies, we continue with our dis-cussion of the HFP data obtained in Experiments 2 and 3of the current study with the assumption that HFP at 4Hz invokes both L+M and L−M pathways.

Given that HFP (at 4 Hz) relies on both the L+M andthe L−M pathways, and that the same is true for HBM(at 0 and 4 Hz), and if we assume that induction effectsfor a given task occur within the pathway(s) that medi-ates the tasks themselves, it might come as no surprisethat the magnitude of the induction effect for HFP andHBM settings were the same in Experiments 2 and 3. Inaddition, given that induction effects sum between the L+M and L−M pathways, and given that induction effectsfor MDB occur only in the L+M pathway (which isthought to be the case; see above), this could explain why,in Experiment 3, the magnitude of induction effects forthe MDB task were significantly smaller than those forthe HFP and HBM tasks. In sum, the pattern of results

observed in Experiments 2 and 3 suggests that inductioneffects occur within the L−M pathway and that these ef-fects sum with the induction effects occurring in the L+M pathway.

A link between HFP and HBM tasks and a dissociationof both tasks with MDB is also supported by the resultsfrom our correlational analyses. Here we found that themagnitude of induction effects on HBM and HFP settingscorrelated positively with each other, but neither corre-lated positively with those observed on MDB settings (seeFig. 5). In fact, we found a significant negative correlationbetween the magnitude of induction effects on MDB (at 0Hz) and HBM (at 0 and 4 Hz) settings. A model of howthis could occur is presented in Fig. 6. Shown are hypo-thetical induction values (in arbitrary units) within theL+M and the L−M pathways for ten hypothetical sub-jects. As described above, we assume that the magnitudeof induction effects observed for each subject is the sum ofthe induction effects within the pathways involved in thetask. Accordingly, for HBM, the predicted magnitude ofinduction is the sum of induction in both the L+M andthe L−M pathways. For MDB, the predicted magnitude ofinduction is the induction in the L+M pathway only. Notethat in order to account for our results, we intentionally

Fig. 6. Hypothetical data producing negative correlation in themagnitude of induction between HBM and MDB. Shown are hy-pothetical induction values (in arbitrary units) within the L+Mand the L−M pathways for ten hypothetical subjects. This modelassumes that the overall induction for each subject is the sum ofinduction within the pathways involved in the task. Accordingly,for HBM the overall induction is the sum of induction in both L+M and L−M. For MDB the overall induction is the induction inthe L+M pathway only. To account for our results (larger magni-tude of induction for HBM than for MDB settings, and an inverserelationship between the magnitude of induction on the twotasks), we intentionally created an inverse relationship betweenthe magnitude of induction occurring within the L+M and L−M pathways. Plotted below is the resulting negative correlationbetween the magnitude of induction on the HBM and MDBtasks.


created an inverse relationship between the amount of in-duction occurring within the L+M versus the L−M path-way. In line with the results from Experiment 3, thismodel produces (1) larger induction effects on the HBMtask than on the MDB task and (2) a negative correlationbetween the magnitude of induction on the HBM andMDB tasks. Interestingly, our data therefore suggest thatsubjects with a greater-than-average amount of inductionwithin the L+M pathway tend to have a lower-than-average amount of induction in the L−M pathway (andvice versa). Further studies will be required for testingthis hypothesis.

In sum, the results of these psychophysical experi-ments demonstrate significant effects of induction onHBM settings and on two other tasks that do not rely onmaking brightness matches, HFP and MDB. The fact thatinduction effects were observed for conditions that shouldeliminate contribution from the L−M pathway (i.e., HFPat high temporal frequencies in Experiment 1 and MDBin Experiment 3) suggest that induction can occur solelywithin the L+M pathway. In addition, given that HFPand HBM at low temporal frequencies rely on both L+Mand L−M pathways, the fact that the magnitudes of in-duction effects for HFP and HBM (at low temporal fre-quencies) were comparable to each other yet significantlylarger than those observed for MDB (Experiments 2 and3) suggests additional induction occurring within theL−M pathway.

ACKNOWLEDGMENTSThis work was supported by NIH grant EY12153 (KRD)and the Oberlin College Neuroscience Department (KLG).We thank Ione Fine for helping us in using Matlab, JayNeitz for the loan of his VSG 2/4 card (Experiments 2 and3), and Bryan D. Alvarez for help running the subjects.We also thank the Pokorny, Smith, and Shevell laborato-ries for helpful discussions, and two reviewers for sugges-tions that greatly improved this paper.

Corresponding author: Karen R. Dobkins, Departmentof Psychology, Mail Stop 0109, University of California,San Diego, La Jolla, California 92093; e-mail:[email protected].

*Present address, Department of Ophthalmology,Medical College of Wisconsin, Milwaukee, Wisconsin53226.

REFERENCES1. M. E. Chevreul, The Principles of Harmony and Contrast of

Colors and Their Applications to the Arts, Original EnglishTranslation 1854; republished in 1967 (Reinhold, 1839).

2. E. G. Heinemann, “Simultaneous brightness induction as afunction of inducing- and test-field luminances,” J. Exp.Psychol. 50, 89–96 (1955).

3. E. G. Heinemann, “The relation of apparent brightness tothe threshold for differences in luminance,” J. Exp.Psychol. 61, 389–399 (1961).

4. E. W. Yund and J. C. Armington, “Color and brightnesscontrast effects as a function of spatial variables,” VisionRes. 15, 917–929 (1975).

5. S. K. Shevell, I. Holliday, and P. Whittle, “Two separate

neural mechanisms of brightness induction,” Vision Res.32, 2331–2340 (1992).

6. H. G. Sperling and W. G. Lewis, “Some comparisonsbetween foveal spectral sensitivity data obtained at highbrightness and absolute threshold,” J. Opt. Soc. Am. 49,983–989 (1959).

7. V. C. Smith and J. Pokorny, “Spectral sensitivity of thefoveal cone photopigments between 400 and 500 nm,”Vision Res. 15, 161–171 (1975).

8. M. Ikeda and H. Shimozono, “Luminous efficiencyfunctions determined by successive brightness matching,”J. Opt. Soc. Am. 68, 1767–1771 (1978).

9. J. Kremers, H. P. N. Scholl, H. Knau, T. T. J. M.Berendschot, T. Usui, and L. T. Sharpe, “L/M cone ratios inhuman trichromats assessed by psychophysics,electroretinography, and retinal densitometry,” J. Opt. Soc.Am. A 17, 517–526 (2000).

10. R. M. Boynton and P. K. Kaiser, “Vision: the additivity lawmade to work for heterochromatic photometry withbipartite fields,” Science 161, 366–368 (1968).

11. A. Eisner and D. I. A. MacLeod, “Blue sensitive cones donot contribute to luminance,” J. Opt. Soc. Am. 70, 121–123(1980).

12. R. M. Boynton, R. T. Eskew, and C. X. Olson, “Blue conescontribute to border distinctness,” Vision Res. 25,1349–1352 (1985).

13. A. Stockman, D. I. A. MacLeod, and D. D. DePriest, “Thetemporal properties of the human short-wavephotoreceptors and their associated pathways,” Vision Res.31, 189–208 (1991).

14. K. L. Gunther and K. R. Dobkins, “Individual differences inchromatic (red/green) contrast sensitivity are constrainedby the relative number of L- versus M-cones in the eye,”Vision Res. 42, 1367–1378 (2002).

15. K. R. Dobkins, K. L. Gunther, and D. H. Peterzell, “Whatcovariance mechanisms underlie green/red equiluminance,luminance contrast sensitive and chromatic (green/red)contrast sensitivity?” Vision Res. 40, 613–628(2000).

16. B. B. Lee, P. R. Martin, and A. Valberg, “The physiologicalbasis of heterochromatic flicker photometry demonstratedin the ganglion cells of the macaque retina,” J. Physiol.(London) 404, 323–347 (1988).

17. R. M. Boynton and P. K. Kaiser, “Temporal analog of theminimally distinct border,” Vision Res. 18, 111–113 (1978).

18. B. Blakeslee and M. E. McCourt, “Similar mechanismsunderlie simultaneous brightness contrast and gratinginduction,” Vision Res. 37, 2849–2869 (1997).

19. D. H. Peterzell, J. S. Werner, and P. S. Kaplan, “Individualdifferences in contrast sensitivity functions: longitudinalstudy of 4-, 6- and 8-month-old human infants,” Vision Res.35, 961–979 (1995).

20. M. Aguilar and W. S. Stiles, “Saturation of the rodmechanism of the retina at high levels of stimulation,” Opt.Acta 1, 59–65 (1954).

21. J. D. Conner and D. I. A. MacLeod, “Rod photoreceptorsdetect rapid flicker,” Science 195, 698–699 (1977).

22. T. N. Wiesel and D. H. Hubel, “Spatial and chromaticinteractions in the lateral geniculate body of the rhesusmonkey,” J. Neurophysiol. 29, 1115–1156 (1966).

23. V. Virsu and B. B. Lee, “Light adaptation in cells ofmacaque lateral geniculate nucleus and its relation tohuman light adaptation,” J. Neurophysiol. 50, 864–878(1983).

24. H. Sun, J. Pokorny, and V. C. Smith, “Rod-cone interactionsassessed in inferred magnocellular and parvocellularpostreceptoral pathways,” J. Vision 1, 42–54 (2001).

25. H. deVries, “The heredity of the relative numbers of redand green receptors in the human eye,” Genetica (TheHague, Neth.) 24, 199–212 (1948).

26. M. L. Bieber, J. M. Kraft, and J. S. Werner, “Effects ofknown variations in photopigments on L/M cone ratiosestimated from luminous efficiency functions,” Vision Res.38, 1961–1966 (1998).

27. B. B. Lee, P. R. Martin, and A. Valberg, “Sensitivity of


macaque retinal ganglion cells to chromatic and luminanceflicker,” J. Physiol. (London) 414, 223–243 (1989).

28. B. B. Lee, J. Pokorny, V. C. Smith, P. R. Martin, and A.Valberg, “Luminance and chromatic modulation sensitivityof macaque ganglion cells and human observers,” J. Opt.Soc. Am. A 7, 2223–2236 (1990).

29. M. Gur and D. M. Snodderly, “A dissociation between brainactivity and perception: chromatically opponent corticalneurons signal chromatic flicker that is not perceived,”Vision Res. 37, 377–382 (1997).

30. G. Wagner and R. M. Boynton, “Comparison of fourmethods of heterochromatic photometry,” J. Opt. Soc. Am.62, 1508–1515 (1972).

31. P. K. Kaiser, B. B. Lee, P. R. Martin, and A. Valberg, “Thephysiological basis of the minimally distinct borderdemonstrated in the ganglion cells of the macaque retina,”J. Physiol. (London) 422, 153–183 (1990).

32. J. Thornton and E. N. Pugh, Jr., “Red/green coloropponency at detection threshold,” Science 219, 191–193(1983).

33. L. Kerr, “Effect of chromatic contrast on stimulusbrightness,” Vision Res. 16, 463–468 (1976).

34. C. Ware, “Evidence for an independent luminancechannel,” J. Opt. Soc. Am. 73, 1379–1382 (1983).

35. M. A. Webster and J. D. Mollon, “Contrast adaptationdissociated different measures of luminance efficiency,” J.Opt. Soc. Am. A 10, 1332–1340 (1993).

36. S. L. Guth, N. J. Donley, and R. T. Marrocco, “Onluminance additivity and related topics,” Vision Res. 9,537–575 (1969).

37. S. L. Guth and H. R. Lodge, “Heterochromatic additivity,foveal spectral sensitivity and a new color model,” J. Opt.Soc. Am. 63, 450–462 (1973).

38. H. Yaguchi and M. Ikeda, “Subadditivity andsuperadditivity in heterochromatic brightness matching,”Vision Res. 23, 1711–1718 (1983).

39. H. Yaguchi and M. Ikeda, “Contribution of opponent-colourchannels to brightness,” in Colour Vision, J. D. Mollon andL. T. Sharpe, eds. (Academic, 1983), pp. 353–360.

40. E. Miyahara, J. Pokorny, and V. C. Smith, “Incrementthreshold and purity discrimination spectral sensitivities ofX-chromosome-linked color defective observers,” VisionRes. 36, 1597–1613 (1996).

41. P. Whittle, “The brightness of coloured flashes on

backgrounds of various colours and luminances,” VisionRes. 13, 621–638 (1973).

42. L. E. Marks, “Blue-sensitive cones can mediate brightness,”Vision Res. 14, 1493–1494 (1974).

43. M. Kalloniatis and M. J. Pianta, “L and M cone input intospectral sensitivity functions: a reanalysis,” Vision Res. 37,799–811 (1997).

44. A. F. Rossi, C. D. Rittenhouse, and M. A. Paradiso, “Therepresentation of brightness in primary visual cortex,”Science 273, 1104–1107 (1996).

45. A. F. Rossi and M. A. Paradiso, “Neural correlates ofperceived brightness in the retina, lateral geniculatenucleus, and striate cortex,” J. Neurosci. 19, 6145–6156(1999).

46. M. Kinoshita and H. Komatsu, “Neural representation ofthe luminance and brightness of a uniform surface in theMacaque primary visual cortex,” J. Neurophysiol. 86,2559–2570 (2001).

47. D. G. Albrecht, “Visual cortex neurons in monkey and cat:effect of contrast on the spatial and temporal phasetransfer functions,” Visual Neurosci. 12, 1191–1210 (1995).

48. T. J. Gawne, T. W. Kjaer, and B. J. Richmond, “Latency:another potential code for feature binding in striate cortex,”J. Neurophysiol. 76, 1356–1360 (1996).

49. J. B. Levitt, R. A. Schumer, S. M. Sherman, P. D. Spear,and J. A. Movshon, “Visual response properties of neuronsin the LGN of normally reared and visually deprivedmacaque monkeys,” J. Neurophysiol. 85, 2111–2129 (2001).

50. S. Magnussen and A. Glad, “Temporal frequencycharacteristics of spatial interaction in human vision,” Exp.Brain Res. 23, 519–528 (1975).

51. M. A. Paradiso and S. Hahn, “Filling-in percepts producedby luminance modulation,” Vision Res. 36, 2657–2663(1996).

52. A. F. Rossi and M. A. Paradiso, “Temporal limits ofbrightness induction and mechanisms of brightnessperception,” Vision Res. 36, 1391–1398 (1996).

53. R. L. DeValois, M. A. Webster, K. K. DeValois, and B.Lingelbach, “Temporal properties of brightness and colorinduction,” Vision Res. 26, 887–897 (1986).

54. A. G. Shapiro, A. D. D’Antona, J. P. Charles, L. A. Belano,J. B. Smith, and M. Shear-Heyman, “Induced contrastasynchronies,” J. Vision 4, 459–468 (2004).


induction effects for heterochromatic brightness matching, heterochromatic flicker photometry, and...

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